Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. In this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy ZS, and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy ZS, and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
There has always been a desire to port high-fidelity reactive flow models from one code to another. For example, the AWE reactive burn model known as CREST has been or is being implemented in several of the U.S. Department of Energy hydrocodes. Those involved with reactive burn model implementation recognize the challenges immediately, e.g., Eulerian versus Lagrangian frameworks, the form of the equation of state, the closure relations, etc. In this work, we report the development of the CREST reactive burn model in CTH, a multidimensional, multi-material hydrocode developed by Sandia National Laboratories, following an earlier implementation shown at the last International Detonation Symposium. Results include code-to-code comparisons between CTH and the AWE hydrocode PERUSE, focusing on the simulated particle velocity histories during a shock-to-detonation transition, and corresponding to previous gas gun impact experiments as well as new model verification studies. Lessons learned are provided, including discussions of the numerical accuracy, in addition to the role of artificial viscosity and artificial viscous work. Finally, simulation results are shown to compare the Snowplough versus P-Alpha porosity model options.
Vapor-deposited PETN films undergo significant microstructure evolution when exposed to elevated temperatures, even for short periods of time. This accelerated aging impacts initiation behavior and can lead to chemical changes as well. In this study, as-deposited and aged PETN films are characterized using scanning electron microscopy and ultra-high performance liquid chromatography and compared with changes in initiation behavior measured via a high-throughput experimental platform that uses laser-driven flyers to sequentially impact an array of small explosive samples. Accelerated aging leads to rapid coarsening of the grain structure. At longer times, little additional coarsening is evident, but the distribution of porosity continues to evolve. These changes in microstructure correspond to shifts in the initiation threshold and onset of reactions to higher flyer impact velocities.
Explosives exposed to conditions above the Chapman-Jouget (CJ) state exhibit an overdriven response that is transient. Reactive flow models are often fit to the CJ conditions, and they transition to detonation based on inputs lower than or near CJ, but these models may also be used to predict explosive behavior in the overdriven regime. One scenario that can create a strongly overdriven state is a Mach stem shock interaction. These interactions can drive an already detonating or transitioning explosive to an overdriven state, and they can also cause detonation at the interaction location where the separate shocks may be insufficient to detonate the material. In this study, the reactive flow model XHVRB utilizing a Mie-Grüneisen equation of state (EOS) for the unreacted explosive, and a Sesame table for the reacted products, will be used to examine Mach stem interactions from multi-point detonation schemes in CTH. The effect of the overdriven response driven by PETN-based explosive pellets will be tracked to determine the transient detonation behavior, and the predicted states from the burn model will be compared to previously published data.
For reactive burn models in hydrocodes, an equilibrium closure assumption is typically made between the unreacted and product equations of state. In the CTH [1] (not an acronym) hydrocode the assumption of density and temperature equilibrium is made by default, while other codes make a pressure and temperature equilibrium assumption. The main reason for this difference is the computational efficiency in making the density and temperature assumption over the pressure and temperature one. With fitting to data, both assumptions can accurately predict reactive flow response using the various models, but the model parameters from one code cannot necessarily be used directly in a different code with a different closure assumption. A new framework is intro-duced in CTH to allow this assumption to be changed independently for each reactive material. Comparisons of the response and computational cost of the History Variable Reactive Burn (HVRB) reactive flow model with the different equilibrium assumptions are presented.
The notion of plane shock waves is a macroscopic, very fruitful idealization of near discontinuous disturbance propagating at supersonic speed. Such a picture is comparable to the picture of shorelines seen from a very high altitude. When viewed at the grain scale where the structure of solids is inherently heterogeneous and stochastic, features of shock waves are non-laminar and field variables, such as particle velocity and pressure, fluctuate. This paper reviews select aspects of such fluctuating nonequilibrium features of plane shock waves in solids with focus on grain scale phenomena and raises the need for a paradigm change to achieve a deeper understanding of plane shock waves in solids.
The propagation of self-sustained formation reactions in sputter-deposited Co/Al multilayers is known to exhibit a design-dependent instability. Multilayers having thin bilayers (<55 nm period) exhibit stable propagating waves, whereas those with a larger period react unstably. The specific two-dimensional (2D) instability observed involves the transverse propagation of a band in front of a stalled front commonly referred to as a “spin band.” Previous finite-element studies have shown that these instabilities are thermodynamically driven by the forward conduction of heat away from the flame front. However, the magnitude of that loss is inherently tied to the bilayer design in traditional bimetallic multilayers, which couples any proposed stability criteria to a varying critical diffusion distance. This work utilizes a recently developed class of materials known as “inert-mediated reactive multilayers” to decouple the thermodynamic and kinetic contributions to propagating wave stability by reducing the stored chemical energy density in normally stable bilayer designs. By depositing an inert product phase (B2-CoAl) within the mid-plane of Co and Al reactant layers, spin instabilities arise as a function of both diluted volume and critical diffusion distance. From there, a stability criterion is determined for Co/Al multilayers based on enthalpy loss from the reaction zone, and its physical significance is explored.
Reactive Co/Al multilayers are uniformly structured materials that may be ignited to produce rapid and localized heating. Prior studies varying the bilayer thickness (i.e., sum of two individual layers of Co and Al) have revealed different types of flame morphologies, including: (a) steady/planar, (b) wavy/periodic, and (c) transverse bands, originating in the flame front. These instabilities resemble the “spin waves” first observed in the early studies of solid combustion (i.e., Ti cylinder in a N2 atmosphere), and are likewise thought to be due to the balance of heat released by reaction and heat conduction forward into the unreacted multilayer. However, the multilayer geometry and three-dimensional (3D) edge effects are relatively unexplored. In this work, a new diffusion-limited reaction model for Co/Al multilayers was implemented in large, novel 3D finite element analysis (FEA) simulations, in order to study the origins of these spinlike flames. This reaction model builds upon previous work by introducing three new phase-dependent property models for: (1) the diffusion coefficient, (2) anisotropic thermal conductivity tensor, and (3) bulk heat capacity, as well as one additional model for the bilayer-dependent heat of reaction. These novel 3D simulations are the first to predict both steady and unsteady flames in Co/Al multilayers. Moreover, two unsteady modes of flame propagation are identified, which depend on the enhanced conduction losses with slower flames, as well as flame propagation around notched edges. Future work will consider the generality of the current modeling approach and also seek to define a more generalized set of stability criteria for additional multilayer systems.
A first-of-its-kind model calibration was performed using Sandia National Laboratories' high-throughput initiation (HTI) experiment for two types of vapor-deposited explosive films consisting of hexanitrostilbene (HNS) or pentaerythritol tetranitrate (PETN). These films exhibit prompt initiation, and they reach steady detonation at sub-millimeter length scales. Following prior work on HNS, we test the hypothesis of approximating these explosive films as fine-grained homogeneous solids with simple Arrhenius kinetics burn models. The model calibration process is described herein using a single-step as well as a two-step Arrhenius rate law, and it consists of systematic parameter sampling leading to a reduction in the model degrees of freedom. Multiple local minima are observed; results are given for seven different optimized parameter sets. Each model set is further evaluated in a two-dimensional simulation of the critical failure thickness for a sustained detonation. Overall, the two-step Arrhenius kinetics model captures the observed behavior for HNS; however, neither model produces a good fit to the PETN data. We hypothesize that the HTI results for PETN correspond to a heterogeneous response, owing to the smaller reaction zone of PETN compared to HNS (i.e., it does not homogenize the fine-grained hot spots as well). Future work should consider using the ignition and growth model for PETN, as well as other reactive burn models such as xHVRB, AWSD, PiSURF, and CREST.
A high-throughput experimental setup was used to characterize initiation threshold and growth to detonation in the explosives hexanitrostilbene (HNS) and pentaerythritol tetranitrate (PETN). The experiment sequentially launched an array of laser-driven flyers to shock samples arranged in a 96-well microplate geometry, with photonic Doppler velocimetry diagnostics to characterize flyer velocity and particle velocity at the explosive-substrate interface. Vapor-deposited films of HNS and PETN were used to provide numerous samples with various thicknesses, enabling characterization of the evolution of growth to detonation. One-dimensional hydrocode simulations were performed with reactions disabled to illustrate where the experimental data deviate from the predicted inert response. Prompt initiation was observed in 144 μm thick HNS films at flyer velocities near 3000 m/s and in 125 μm thick PETN films at flyer velocities near 2400 m/s. This experimental setup enables rapid quantification of the growth of reactions in explosive materials that can reach detonation at sub-millimeter length scales. These data can subsequently be used for parameterizing reactive burn models in hydrocode simulations, as discussed in Paper II [D. E. Kittell, R. Knepper, and A. S. Tappan, J. Appl. Phys. 131, 154902 (2022)].
Energetic materials with different properties can be mixed or layered to control performance. However, reactions at material interfaces are poorly understood and performance may be highly dependent on the degree of mixing. In this work, we use vapor-deposited explosive multilayers as a model system to investigate shock interactions between different explosive materials with precisely controlled spacings. Samples consisted of alternating pentaerythritol tetranitrate (PETN) and hexanitrostilbene (HNS) layers, materials that have substantial differences in detonation velocity, with individual layer thicknesses in the vicinity of the critical thickness for detonation propagation of each material (~100 - 200 μm). Additional experiments on PETN/HNS bilayer samples were conducted to elucidate the role of non-ideal interfaces on detonation propagation. Preliminary hydrocode simulations were employed to simulate detonation performance, using an Arrhenius reactive burn model that was parameterized from detonation velocity and failure data from vapor-deposited films of each constituent material. Measured detonation velocities in the multilayer samples were significantly lower than expected, given that the individual PETN layer thicknesses were larger than the critical thickness for detonation propagation. The bilayer experiments highlight the role of non-ideal interfaces in contributing to this result.
Within the energetics community, considerable effort is being put forth to find a robust scale-bridging link between unreacted material microstructures and the observed material responses, e.g. detonation and sub-detonative phenomena. Specifically, one area where this scale-bridging capability is needed is mesoscale modeling of explosives initiation (MMEI); here, material microstructures are imported directly or as statistical reconstructions into a hydrocode. While MMEI is attractive for simulating the shock initiation process with ever-increasing model fidelity, a large gap remains between the data being generated at the mesoscale and the calibration of burn model parameters. In this work, stochastic burn models are explored as a paradigm-shift to address possible scale-bridging schemes. These stochastic, particle-based methods are similar to those used for granular and droplet-laden flows, with Langevin-type equations. Further parallels are drawn to turbulent combustion modeling and preliminary developments using probability density function (pdf) theory by Baer, Gartling, and DesJardin. In order to implement these new scale-bridging schemes, one example of a stochastic burn model is explained in greater detail. Results from the stochastic burn model and MMEI simulations are given to illustrate the proposed approach. Ultimately, the execution of this work will be a community endeavor; to achieve such a capability, research efforts should focus on full-field data mining and pdf evolution, in addition to new numerical techniques for hydrocodes.
We present an approach and relevant models for predicting the probabilistic shock-to-detonation transition (SDT) behavior and Pop plot (PP) of heterogeneous energetic materials (HEM) via mesoscopic microstructure-explicit (ME) and void explicit (VE) simulations at the millimeter (mm) sample size scale. Although the framework here is general, the particular material considered in this paper is pressed Octahydro-1,3,5,7-tetranitro-1,2,3,5-tetrazocine (HMX). To systematically delineate the effects of material heterogeneities, four material cases are considered. These cases are homogeneous material, material with granular microstructure but no voids, homogeneous material with voids, and material with both granular microstructure and voids. Statistically equivalent microstructure sample sets (SEMSS) are generated and used. Eulerian hydrocode simulations explicitly resolve the material heterogeneities, voids, and the coupled mechanical-thermal-chemical processes. In particular, it is found that both microstructure and voids strongly influence the SDT behavior and PP. The effects of different combinations of microstructure heterogeneity and voids on the SDT process and PP are quantified and rank-ordered. The overall framework uses the Mie–Grüneisen equation of state and a history variable reactive burn model (HVRB). A novel probabilistic representation for quantifying the PP is developed, allowing the calculation of (1) the probability of observing SDT at a given combination of shock pressure and run distance, (2) the run-distance to detonation under a given combination of shock pressure and prescribed probability, and (3) the shock pressure required for achieving SDT at a given run distance with a prescribed probability. The results are in agreement with general trends in experimental data in the literature.
Explosive shock desensitization phenomena have been recognized for some time. It has been demonstrated that pressure-based reactive flow models do not adequately capture the basic nature of the explosive behavior. Historically, replacing the local pressure with a shock captured pressure has dramatically improved the numerical modeling approaches. A pseudo-entropy based formulation using the History Variable Reactive Burn model, as proposed by Starkenberg, was implemented into the Eulerian shock physics code CTH. Improvements in the shock capturing algorithm in the model were made that allow reproduction of single shock behavior consistent with published Pop-plot data. It is also demonstrated to capture a desensitization effect based on available literature data, and to qualitatively capture multi-dimensional desensitization behavior. This model shows promise for use in modeling and simulation problems that are relevant to the desensitization phenomena. Issues are identified with the current implementation and future work is proposed for improving and expanding model capabilities.
We combined the miniature cylinder expansion test (Mini-Cylex), with the Disk Acceleration Test (DAX) using Type K copper, Picatinny Liquid Explosive, and photonic Doppler velocimetry. We estimated the CJ state using plate reverberation methods at the test cap. We extracted velocities at 2, 7, and 10 volume expansions to fit Jones-Wilkins-Lee Equation of State and estimated Gurney velocity at the tube wall. The test also provides an additional method to estimate reaction products Hugoniot through knowledge of the copper test cap. Our experiments and simulations are within expected uncertainty. The test and the analysis effectively reduce costs while keeping or increasing fidelity.
A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.
A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.